Use the image to answer the question.
A number line with arrows at both ends ranges from negative 12 to 12. The numbers negative 12, 0, and 12 are labeled.
Solve the following equation: 22+−20. Use the number line as a model to find the solution.
(1 point)
Responses
−2
negative 2
2
2
42
42
−42
To solve the equation 22+−20, we need to add 22 to -20. Starting at 22 on the number line and moving 20 spaces to the left gives us -2. Therefore, the solution is -2.
What is the sum of −23+−17+10?(1 point)
Responses
30
30
−30
negative 30
50
50
−50
To find the sum of -23, -17, and 10, we add these numbers together.
-23 + -17 + 10 = -30
Therefore, the sum is -30.
Sally saved $26 in January, $19 in February, $47 in March, and $20 in April. How much money has she saved so far this year?(1 point)
To find out how much money Sally has saved so far this year, we add up the amounts she saved each month.
$26 + $19 + $47 + $20 = $112
Therefore, Sally has saved a total of $112 so far this year.
Use the image to answer the question.
A number line with arrows at both the ends ranges from negative 110 to negative 70 in increments of 1, but labeled in increments of 10. A closed circle is placed on negative 75, which is also labeled, and negative 105. A curved arrow is drawn leftward from negative 75 to negative 105.
Which word problem matches the model?
(1 point)
Responses
Miguel has a negative balance in his bank account of $75. He deposited $30 into his account. What is his current balance?
Miguel has a negative balance in his bank account of $75. He deposited $30 into his account. What is his current balance?
Miguel has saved $75. He spent $30 at the store. How much money does he have now?
Miguel has saved $75. He spent $30 at the store. How much money does he have now?
Miguel has a negative balance in his bank account of $75. He spent $25 at the store and was charged an overdraft fee of $5. What is his current balance?
Miguel has a negative balance in his bank account of $75. He spent $25 at the store and was charged an overdraft fee of $5. What is his current balance?
Miguel made $75 mowing lawns and another $30 pulling weeds during the month of May. How much money did he earn?
The word problem that matches the model would be:
Miguel has a negative balance in his bank account of $75. He spent $25 at the store and was charged an overdraft fee of $5. What is his current balance?
Rudy received a bonus of $2,000. He then paid his rent of $775, spent $250 on utilities, and paid his cell phone bill of $82. How much money does Rudy have left from his bonus after paying his bills?(1 point)
Responses
$1,107
$1,107
$975
$975
$893
$893
$3,107
To find out how much money Rudy has left from his bonus after paying his bills, we need to subtract the total amount of money he spent from the amount of his bonus.
Bonus = $2,000
Rent = $775
Utilities = $250
Cell phone bill = $82
Total spent = $775 + $250 + $82 = $1,107
Amount left = $2,000 - $1,107 = $893
Therefore, Rudy has $893 left from his bonus after paying his bills.
Miki is trying to help her younger brother understand why 12−(−5) is equal to 17. She draws a number line to help. Explain how a number line could help to show that 12−(−5) is equal to 17. (1 point)
Responses
Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.
Starting at 12 on the number line, you must move 5 units in the negative direction to get to 7.
Starting at 12 on the number line, you must move 17 units in the negative direction to get to −5.
Starting at 12 on the number line, you must move 17 units in the negative direction to get to negative 5 .
Starting at −5 on the number line, you must move 17 units in the positive direction to get to 12.
Starting at negative 5 on the number line, you must move 17 units in the positive direction to get to 12.
Starting at −5 on a number line, you must move 12 units in the positive direction to get to 17.
To show that 12 - (-5) is equal to 17 using a number line, you would start at 12 on the number line and then move 5 units in the positive direction. This brings you to the number 17.
Therefore, starting at 12 on the number line, you must move 5 units in the positive direction to get to 17.
How can you represent −5⋅−4 with a model?(1 point)
Responses
−5+−5+−5+−5
negative 5 plus negative 5 plus negative 5 plus negative 5
−(−4+−4+−4+−4+−4)
negative left parenthesis negative 4 plus negative 4 plus negative 4 plus negative 4 plus negative 4 right parenthesis
4+4+4+4+4
4 plus 4 plus 4 plus 4 plus 4
5⋅4
To represent -5 * -4 with a model, you would have a line with -5 jumps of length -4.
This can be represented as:
−(-4+−4+−4+−4+−4)
It means you have 5 jumps of length -4, which is the same as multiplying -4 by -5.
Therefore, the model representation for -5 * -4 is −(-4+−4+−4+−4+−4).
Multiply −9⋅(−18).(1 point)
To multiply -9 * (-18), we multiply the two numbers together:
-9 * (-18) = 162
Therefore, -9 * (-18) is equal to 162.
Connect the model −(7+7+7+7+7+7) to the algorithm for solving the multiplication problem it models.(1 point)
Responses
The model represents −6⋅7, which is solved by multiplying 6 times 7 and changing the sign to get −42.
The model represents negative 6 times 7 , which is solved by multiplying 6 times 7 and changing the sign to get negative 42 .
The model represents 6⋅(−7), which is solved by multiplying 6 times 7 and changing the sign to get −42.
The model represents 6 times left parenthesis negative 7 right parenthesis , which is solved by multiplying 6 times 7 and changing the sign to get negative 42 .
The model represents −7⋅6, which is solved by multiplying 7 times 6 and changing the sign to get −42.
The model represents negative 7 times 6 , which is solved by multiplying 7 times 6 and changing the sign to get negative 42 .
The model represents 7⋅(−6), which is solved by multiplying 7 times 6 and changing the sign to get −42.
The model represents 6⋅(−7), which is solved by multiplying 6 times 7 and changing the sign to get −42.
Therefore, the model −(7+7+7+7+7+7) corresponds to the algorithm for solving 6⋅(−7).
What model can you use to represent −30÷−6?(1 point)
Responses
(−6)+(−6)+(−6)+(−6)+(−6)=5(−6)=−30
left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis plus left parenthesis negative 6 right parenthesis equals 5 left parenthesis negative 6 right parenthesis equals negative 30
−30−(−6)−(−6)−(−6)−(−6)−(−6)=−30−5(−6)=0
negative 30 minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis minus left parenthesis negative 6 right parenthesis equals negative 30 minus 5 left parenthesis negative 6 right parenthesis equals 0
30−6−6−6−6−6=30−5(6)
30 minus 6 minus 6 minus 6 minus 6 minus 6 equals 30 minus 5 left parenthesis 6 right parenthesis
(−5)+(−5)+(−5)+(−5)+(−5)+(−5)=6(−5)=−30
To represent −30÷−6 using a model, we can use the repeated subtraction model. We start with -30 and repeatedly subtract -6 until we reach zero.
The model would be:
−6 − 6 − 6 − 6 − 6 − 6 = -30
This shows that when we subtract -6 six times from -30, we get -30 again.
Therefore, the model −6 − 6 − 6 − 6 − 6 − 6 represents -30÷-6.
What is the result of dividing −245÷35?(1 point)
To divide -245 by 35, we have:
-245 ÷ 35 = -7
Therefore, the result of dividing -245 by 35 is -7.
What is the result of the division modeled by −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18)=0?(1 point)
To find the result of the division modeled by −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18) = 0, we need to determine the value of the missing number.
This can be done by adding the given numbers repeatedly until we reach 0:
-108 + (-18) + (-18) + (-18) + (-18) + (-18) + (-18) = 0
Therefore, the result of the division modeled by −108−(−18)−(−18)−(−18)−(−18)−(−18)−(−18) = 0 is satisfied by these values.
Use the image to answer the question.
A number line with arrows at both ends ranges from negative 12 to 12. The numbers negative 12, 0, and 12 are labeled.
Solve the following equation: 22+−20. Use the number line as a model to find the solution.
(1 point)
Responses
−2
negative 2
2
2
42
42
−42
To solve the equation 22 + (-20), we can use the number line as a model.
Starting at 22 on the number line, we move 20 units to the left.
This brings us to the number -2 (-2 is 2 units to the left of 0 on the number line).
Therefore, the solution to 22 + (-20) is -2.
What is the sum of −23+−17+10?(1 point)
Responses
30
30
−30
negative 30
50
50
−50
To find the sum of -23, -17, and 10, we simply add these numbers together.
-23 + -17 + 10 = -30
Therefore, the sum is -30.
Sally saved $26 in January, $19 in February, $47 in March, and $20 in April. How much money has she saved so far this year?(1 point)
$
To find out how much money Sally has saved so far this year, we can add up the amounts she saved each month.
$26 + $19 + $47 + $20 = $112.
Therefore, Sally has saved a total of $112 so far this year.
Rudy received a bonus of $2,000. He then paid his rent of $775, spent $250 on utilities, and paid his cell phone bill of $82. How much money does Rudy have left from his bonus after paying his bills?(1 point)
Responses
$1,107
$1,107
$975
$975
$893
$893
$3,107
To calculate how much money Rudy has left from his bonus after paying his bills, we subtract the total amount of money he spent from his bonus.
Bonus = $2,000
Rent = $775
Utilities = $250
Cell phone bill = $82
Total spent = $775 + $250 + $82 = $1,107
Amount left = $2,000 - $1,107 = $893
Therefore, Rudy has $893 left from his bonus after paying his bills.